Convexity criteria and uniqueness of absolutely minimizing functions

Details Convexity criteria and uniqueness of absolutely minimizing functions Convexity criteria and uniqueness of absolutely minimizing functions

2010-03-16

arxiv.org/abs/1003.3171v1

Mathematics

Analysis of PDEs

34 pages

Scientific paper

We show that absolutely minimizing functions relative to a convex Hamiltonian $H:\mathbb{R}^n \to \mathbb{R}$ are uniquely determined by their boundary values under minimal assumptions on $H.$ Along the way, we extend the known equivalences between comparison with cones, convexity criteria, and absolutely minimizing properties, to this generality. These results perfect a long development in the uniqueness/existence theory of the archetypal problem of the calculus of variations in $L^\infty.$

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